Algebraic families of connected stable nodal curves with genus \(g\)  and
\(n\)  markings form the objects of a smooth Deligne-Mumford stack
\(\overline{M}_{g,n}\)  [1]} which admits a coarse moduli space with
the structure of a normal projective variety. The maps
\(\operatorname{Def}({\Sigma }) \rightarrow \overline{M}_{g,n}, \ s \mapsto [{\Sigma }_s] \) 
(restricted to a neighborhood of 0) provide \(\overline{M}_{g,n}\)  with an
atlas of holomorphic orbifold charts.
